A new Monte Carlo approach to diffusion in constricted porous geometries

A method for simulating trajectories of particles undergoing Brownian motion in constricted domains is introduced. This method does not rely on discretization of the domain, and the computed trajectories are statistically equivalent to the trajectories of real Brownian particles. The stepsize is optimized over a continuum, making the method very efficient. The method is applied to study diffusion retardation in constricted, two-dimensional domains that represent idealized porous media. The effects of pore geometric parameters such as number of outlets per pore (n_T), throat width (w), and throat length (z) are investigated. A retardation factor (R_p) is defined as the ratio of the average time required for a Brownian particle to pass through a constricted pore, to the average time required for a similar particle to pass through an unconstricted pore of equal length. For the class of pores studied, the empirical relation R_p ∼ [w/W]^-β/n_T, where W is the central pore body diameter, provides a reasonable fit to the simulation results. The exponent β increases with z/W.